Existence and uniqueness of weak solutions to a parabolic nonlocal 1-Laplacian equation

Dingding Li; Chao Zhang

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arXiv · 2406.19020

Existence and uniqueness of weak solutions to a parabolic nonlocal 1-Laplacian equation

Dingding Li·Chao Zhang

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Abstract

We consider a class of parabolic nonlocal $1$-Laplacian equation \begin{align*} u_t+(-\Delta)^s_1u=f \quad \text{ in }\Omega\times(0,T]. \end{align*} By employing the Rothe time-discretization method, we establish the existence and uniqueness of weak solutions to the equation above. In particular, different from the previous results on the local case, we infer that the weak solution maintains $\frac{1}{2}$-H\"{o}lder continuity in time.

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Dingding Li, Chao Zhang. 2024-06-27. Existence and uniqueness of weak solutions to a parabolic nonlocal 1-Laplacian equation. https://arxiv.org/abs/2406.19020

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